How do you know when you're bored?

For player and listener alike the answer is the same: When your mind wanders, or simply turns off.

What "mind?"  This is the interesting part.  We have all kinds of minds.  The one addressed by Music Appreciation is not, to my taste, relevant to playing or listening to music.  Identifying themes and subthemes is a distraction from other mental activities that define listening.

A good example comes readily to mind: Last night I was listening to the radio.  Strictly by chance I heard announced a recording by the Belcea string quartet of Schubert's Death and the Maiden quartet.  What were my first reactions?  a) Recordings are not my preferred listening   b) Another cliche reading of that over-done piece?  c) Yes, but the Belcea is a very fine ensemble.  So I listened.

It took less than a minute to realize that the Belcea was giving me no choice but to listen for every nuance of their superior playing:  Not a trace of a cliche; every single note intoned purposefully, every event personal without a trace of sentimentality.  The piece flew by, a new important definition of paying attention.

For all their virtuosity they played as if they had never heard or played that work before.  No trace of boredom there.